The rules for general context are very well described in the other answers, but I just wanted to add something for mailing rules (from where I work, but I assume we aren't the only mass printing company with such rules)  :

• known gender [M] --> Cher client,

• known gender [F] --> Chère cliente,

• unknown gender --> Chère cliente, Cher client,

Here, the need to be affable with your customers (who are more often female than male in many activities) has changed the slightly aged rule of Le masculin l'emporte sur le féminin...

The rules for general context are very well described in the other answers, but I just wanted to add something for mailing rules (from where I work, but I assume we aren't the only mass printing company with such rules):

• known gender (M) ⟶ Cher client,

• known gender (F) ⟶ Chère cliente,

• unknown gender ⟶ Chère cliente, Cher client,

Here, the need to be affable with your customers (who are more often female than male in many activities) has changed the slightly aged rule of Le masculin l'emporte sur le féminin…